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Geometric Studies on Mittag-Leffler Type Function Involving a New Integrodifferential Operator

Author

Listed:
  • F. Ghanim

    (Department of Mathematics, College of Science, University of Sharjah, Sharjah P.O. Box 27272, United Arab Emirates)

  • Hiba F. Al-Janaby

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq)

  • Marwan Al-Momani

    (Department of Mathematics, College of Science, University of Sharjah, Sharjah P.O. Box 27272, United Arab Emirates)

  • Belal Batiha

    (Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan)

Abstract

The generalized exponential function in a complex domain is called the Mittag-Leffler function (MLF). The implementations of MLF are significant in diverse areas of science. Over the past few decades, MLF and its analysis with generalizations have become an increasingly rich research area in mathematics and its allied fields. In the geometric theory of meromorphic functions, the main contribution to this discipline of study is to enrich areas of operator theory on complex punctured domains and differential complex inequalities, namely, subordination theory. This effort presents integrodifferential operator of meromorphic functions in the punctured unit disk. It is formulated by combining the differential operator and the integral operator correlating with the extended generalized Mittag-Leffler function. Furthermore, some interesting geometric features in terms of the subordination principle are investigated.

Suggested Citation

  • F. Ghanim & Hiba F. Al-Janaby & Marwan Al-Momani & Belal Batiha, 2022. "Geometric Studies on Mittag-Leffler Type Function Involving a New Integrodifferential Operator," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3243-:d:908650
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    References listed on IDEAS

    as
    1. Rakesh K. Parmar, 2015. "A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus," Mathematics, MDPI, vol. 3(4), pages 1-14, November.
    2. Firas Ghanim & Khalifa Al-Shaqsi & Maslina Darus & Hiba Fawzi Al-Janaby, 2021. "Subordination Properties of Meromorphic Kummer Function Correlated with Hurwitz–Lerch Zeta-Function," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    3. Aabed Mohammed & Maslina Darus, 2011. "Starlikeness Properties of a New Integral Operator for Meromorphic Functions," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-8, July.
    4. Hari M. Srivastava & Arran Fernandez & Dumitru Baleanu, 2019. "Some New Fractional-Calculus Connections between Mittag–Leffler Functions," Mathematics, MDPI, vol. 7(6), pages 1-10, May.
    5. Hiba Al-Janaby & Firas Ghanim & Maslina Darus, 2020. "On The Third-Order Complex Differential Inequalities of ξ -Generalized-Hurwitz–Lerch Zeta Functions," Mathematics, MDPI, vol. 8(5), pages 1-21, May.
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    Cited by:

    1. Alina Alb Lupaş, 2023. "Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    2. Faten Fakher Abdulnabi & Hiba F. Al-Janaby & Firas Ghanim & Alina Alb Lupaș, 2023. "Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    3. Jordanka Paneva-Konovska, 2022. "Taylor Series for the Mittag–Leffler Functions and Their Multi-Index Analogues," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

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